Freedman, Michael H. Whitehead\(_ 3\) is a “slice” link. (English) Zbl 0678.57002 Invent. Math. 94, No. 1, 175-182 (1988). In this paper it is shown that the Whitehead double Wh(L) of a two component link L is slice (topologically flat) if and only if the linking number of L is zero. In particular \(Wh_ 3=Wh(Wh_ 1)\) is slice. Here \(Wh_ 1\) is the Whitehead double of the Hopf link. This case acts as a marker for the general case. The slicing is obtained by building abstractly a 4-manifold with appropriate boundary and then performing surgery. This has to be done by hand rather than quoting a surgery theorem since the relevant fundamental group F(x,y) has exponential growth. Reviewer: R.A.Fenn Cited in 2 ReviewsCited in 6 Documents MSC: 57M25 Knots and links in the \(3\)-sphere (MSC2010) 57N13 Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010) 57R65 Surgery and handlebodies Keywords:Whitehead double of a two component link; slice links; linking number; 4- manifold; surgery PDFBibTeX XMLCite \textit{M. H. Freedman}, Invent. Math. 94, No. 1, 175--182 (1988; Zbl 0678.57002) Full Text: DOI EuDML References: [1] [C] Cochran, T.: Concordance Invariance of Coefficients of Conway’s Link Polynomial. Invent. Math.82, 527-541 (1985) · Zbl 0589.57005 [2] [F1] Freedman, M.: A new technique for the link slice problem. Invent. Math.80, 453-465 (1985) · Zbl 0569.57002 [3] [F2] Freedman, M.: The disk theorem for four-dimensional manifolds. Proc. Int. Congr. Math. 647-663 (1983) [4] [FQ] Freedman, M., Quinn, F.: A quick proof of the 4-dimensional stable surgery theorem. Comment. Math. Adv.55, 668-671 (1983) · Zbl 0453.57024 [5] [M] Milnor, J.: Link groups. Ann. Math.59, 177-195 (1954) · Zbl 0055.16901 [6] [CG] Casson, A., Gordon, C.: On slice knots in dimension three. Proc. Symp. Pure Math.32, Am. Math. Soc. Providence, R.I., 39-54 (1978) [7] [S] Stallings, J.: Homology and central series of groups. J. Algebra2, 70-181 (1965) · Zbl 0135.05201 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.